Autopopulate Cells

Hello all,
After a bit of googling and searching these forums, I can't quite find an answer to what seems like a pretty simple problem.

I have a list of around 20 companies that belong to either Group A, or Group B. These companies and their groups are listed in Column A (Company) and Column B (Group) on Worksheet B;

Company Name........Company Group
Name 1...................Group A
Name 2...................Group A
Name 3...................Group B
Name 4...................Group A
Name 5...................Group B
etc..........................etc

On Worksheet A, in Column A, company names (that match company names on Worksheet B) are manually entered. I would like Column B to populate with the company's group as defined on Worksheet B, Column B automatically. This is to speed up data entry, so the person entering each company doesn't have to remember, or look up that company's group (A or B).

In short, if I enter "Name 3" in Column A, I would like Column B to automatically populate with the text "Group B" as defined on Worksheet B.

I'm not quite sure where to begin. Company names will be added and removed from time to time, so ideally I would just update Worksheet B and those changes would be reflected on Worksheet A.

Any help would be greatly appreciated.

Thanks.

Thanks lychee. Worksheet B looks like this;

Company Name..........Group
Company 1................A
Company 2................A
Company 3................B
Company 4................A
Company 5................B
Company 6................B
Company 7................B

However, on Worksheet A, using that formula, my results are always "A", regardless of Company entered, like this;

Company Name..........Group
Company 1................A
Company 6................A
Company 7................A
Company 1................A
Company 7................A

Maybe I didn't explain things properly in my OP? What I want to happen is if I type "Company 7" anywhere in Column A on Worksheet A, the result will be Column B being populated with "B" (the group defined on Worksheet B).

Thanks.

The formula as it is written in the post will only work for the data in cell A1. If you have data in cell A2-A7, you have to fill down the formula, which would change it to:

=INDEX('Worksheet B'!B:B,MATCH('Worksheet A'!A2,'Worksheet B'!A:A,0))
=INDEX('Worksheet B'!B:B,MATCH('Worksheet A'!A3,'Worksheet B'!A:A,0))
=INDEX('Worksheet B'!B:B,MATCH('Worksheet A'!A4,'Worksheet B'!A:A,0))
and so on.

Works perfectly. Thanks lychee.